Problem: Solve for $x$ and $y$ using substitution. ${5x+3y = 1}$ ${x = 3y+11}$
Answer: Since $x$ has already been solved for, substitute $3y+11$ for $x$ in the first equation. ${5}{(3y+11)}{+ 3y = 1}$ Simplify and solve for $y$ $15y+55 + 3y = 1$ $18y+55 = 1$ $18y+55{-55} = 1{-55}$ $18y = -54$ $\dfrac{18y}{{18}} = \dfrac{-54}{{18}}$ ${y = -3}$ Now that you know ${y = -3}$ , plug it back into $\thinspace {x = 3y+11}\thinspace$ to find $x$ ${x = 3}{(-3)}{ + 11}$ $x = -9 + 11$ ${x = 2}$ You can also plug ${y = -3}$ into $\thinspace {5x+3y = 1}\thinspace$ and get the same answer for $x$ : ${5x + 3}{(-3)}{= 1}$ ${x = 2}$